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Gray
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Homework Statement
Let C|+-> = +-|+->, and consider a state |psi> = cosT|+> + sinT|->. Find T such that the product of uncertainties, deltaAdeltaB, vanishes (i.e. becomes zero).
*Note: +- means plus or minus repectively.
Homework Equations
[A,B] = iC
In a previous question I proved deltaAdeltaB>=1/2|<psi|C|psi>| using the Schwarz inequality and some other stuff.
The Attempt at a Solution
So we want 1/2|<psi|C|psi>| = 0.
i.e. |<psi|CcosT|+> + <psi|CsinT|->| = 0.
Then I assumed <psi| = +|cosT + <-|sinT similarly to the psi ket.
So
|<+|(cosT)^2.C|+> + <-|sinT.C.cosT|+> + <+|cosT.C.sinT|-> + <-|(sinT)^2.C|->| = 0
Then use C|+-> = +-|+-> and similarly I assumed <+-|C = <+-|+- for the C bra.
So
|<+|(cosT)^2|+> + <-|sinTcosT|+> + <+|cosTsinT|-> + <-|(sinT)^2|->| = 0
|(cosT)^2 + sinTcosT<-|+> + sinTcosT<+|-> + (sinT)^2| = 0
|(cosT)^2 - sinTcosT<+|-> + sinTcosT<+|-> + (sinT)^2| = 0
|(cosT)^2 + (sinT)^2| = 0
which is clearly nonsense.
Are my assumptions incorrect? Am I not allowed to convert the ket formalism to the bra formalism in this manner?
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